Table Of ContentMOLECULAR BIOLOGY
An International Series of Monographs and Textbooks
Editors: BERNARD HORECKER, NATHAN O. KAPLAN, JULIUS MARMUR, AND
HAROLD A. SCHERAGA
A complete list of titles in this series appears at the end of this volume.
ENZYME CATALYSIS
AND REGULATION
Gordon G. Hammes
Department of Chemistry
Cornell University
Ithaca, New York
1982
ACADEMIC PRESS
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COPYRIGHT © 1982, BY ACADEMIC PRESS, INC.
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Library of Congress Cataloging in Publication Data
Hammes, Gordon G., Date
Enzyme catalysis and regulation.
(Molecular biology series)
includes bibliographical references and index.
1. Enzymes. 2. Biological control systems.
I. Title. II. Series.
QP601.H26 574.19'25 82-1597
ISBN 0-12-321962-0 paper AACR2
ISBN 0-12-321960-4 cloth
PRINTED IN THE UNITED STATES OF AMERICA
82 83 84 85 9 8 7 6 5 4 3 2 1
Preface
This book is based on a course which I have been teaching on and off for
16 years. The course is intended for graduate students and advanced
undergraduates. The principle difficulty I have encountered in writing this
book (and in giving the course) was deciding what not to include. My
desire is to have a book of reasonable size which well-prepared under-
graduate and graduate students can use as an introduction to enzyme
catalysis and regulation. At the same time, I have tried to make this book
sufficiently up to date so as to be a useful reference for research workers.
My belief is that if the material in this book is understood, no difficulty
should be encountered in reading current literature on enzyme mecha-
nisms. Unfortunately, in order to attain my goal of a reasonable size book,
some important topics are necessarily omitted and only a curtailed discus-
sion of others is presented. However, I hope that the scope and excite-
ment of modern research on enzymes is evident.
Some background in biochemistry is assumed so that the first chapter
on enzyme structure is relatively brief. The next chapter, which discusses
methods of probing enzyme structure, also is not long; a complete discus-
sion would require several additional volumes. Kinetic methods are dis-
cussed in some detail, although no attempt is made to provide a compen-
dium of rate laws. Instead the emphasis is on general principles of
steady-state and transient kinetics. An overall discussion of enzyme
catalysis then attempts to draw together the chemical principles involved.
Case studies of a few well-documented enzymes are presented next to
illustrate the methods and principles developed earlier. The next two
X Preface
chapters are concerned with the regulation of enzyme activity from a
nongenetic viewpoint: this includes a comprehensive discussion of binding
isotherms and models for allosterism. Two particular enzymes are utilized
as examples of well-studied regulatory enzymes. The last two chapters
cover special topics of current interest, namely multienzyme complexes
and membrane-bound enzymes. Finally a brief compendium of student-
tested problems is provided in the appendix.
I am indebted to many colleagues for their critical comments on por-
tions of the manuscript and for many stimulating discussions. I would
especially like to acknowledge G. P. Hess, H. A. Scheraga, P. R. Schim-
mel, D. A. Usher, and C.-W. Wu. I am indebted to Dr. Richard Feldmann
of the National Institutes of Health for the stereo representations of pro-
tein structures in Chapter 7. Chapter 8 is based on a review by C.-W. Wu
and myself [Anna. Rev. Biophys. Bioeng. 3, 1 (1974)] and Chapter 10 is
based on a review appearing in Biochem. Soc. Symp. 46 (1981). I would
like to thank Dr. Wu, Annual Reviews Inc., and the Biochemical Society
for their permission to use portions of the original material. Special thanks
are due to my wife, Judy, for her assistance in proofreading and to Joanne
Widom for preparation of the index.
The preparation of this manuscript would not have been possible with-
out the very able technical assistance of Connie Wright, Joan Roberts,
and Jean Scriber. Since this book is a reflection of my research interests, I
would like to acknowledge the financial assistance of the National Insti-
tutes of Health and the National Science Foundation, who have supported
my research for many years.
Gordon G. Hammes
1
Protein Structure and Dynamics
Since all enzymes are proteins, a logical starting point for the discussion
of enzymes is to consider the general features of protein structure. Features
of particular interest to enzymology are considered. This topic is treated more
fully in some of the references at the end of the chapter.
The primary structure of a protein is specified by the order in which the
amino acids are linked together through peptide bonds. The most important
feature of this structure is the peptide linkage shown in Fig. 1-1. Because of
resonance, which gives the N—C bond some double bond character, the
peptide bond is planar. Furthermore, the a carbons are always trans. These
two features of the peptide bond play a dominant role in determining protein
structure. The other covalent linkage of importance is the disulfide bond that
joins different parts of the protein chain. Special note also should be made
of the imino acids (e.g., proline), which create a very rigid peptide bond. The
final structure of a protein is determined by the above factors and optimiza-
tion of noncovalent interactions involving the peptide backbone and the
amino acid side chains. The large variety of amino acid side chains provides
the possibility of several different types of noncovalent interactions, namely,
van der Waals, pi electron stacking, hydrogen bonding, and electrostatic. In
addition, some of these side chains are important in enzymes as acid-base
catalysts. The main types of amino acid side chains and their functions are
summarized in Table 1-1.
H R tf
V II
Fig. 1-1. The planar and trans peptide bond with
standard bond distances in Angstroms. *ï " j \ a
H R H
3.8 A H
1
2 1 Protein Structure and Dynamics
Table 1-1
Amino Acid Side Chains and Their Function
Side chain group Amino acids Functions and interactions
Hydrocarbon Alanine, leucine van der Waals
Aromatic Phenylalanine, tyrosine, van der Waals, pi electron
tryptophan stacking
Carboxyl Aspartate, glutamate Electrostatic, hydrogen bonding,
acid-base catalysis
Amino Lysine, arginine Electrostatic, hydrogen bonding,
acid-base catalysis
Imidazole Histidine Electrostatic, hydrogen bonding,
acid-base catalysis, van der
Waals, pi electron stacking
Hydroxyl Serine, threonine, Hydrogen bonding, acid-base
tyrosine catalysis
Amide Asparagine, glutamine Hydrogen bonding
Sulfhydryl Cysteine Hydrogen bonding, electrostatic,
acid-base catalysis
To gain further insight into the nature of protein structure, noncovalent
interactions are considered in more detail. Potentially the largest amounts
of energy are available from electrostatic interactions. For example, the en-
ergy of interaction between two univalent charges is e2/sr, where e is the
charge of an electron, ε is the dielectric constant, and r is the distance between
thfe charges. In water (ε = 80) for charge separations of a few Angstroms, the
energy is a few kilocalories per mole. The correct dielectric constant to use
when considering protein structures is not obvious, but is probably some-
where between that of water and organic solvents (ε ~ 3). Thus the energies
involved could be substantial, particularly if the dielectric constant is low
and/or clusters of charges are present in the protein. For ions and dipoles,
the energy of interaction is z^cos θ/sr2, where z is the charge, μ is the dipole
moment, and Θ is a dipole orientation angle. In water for a univalent charge,
a dipole moment of a few Debyes, and a separation distance of a few
Angstroms, the energy of interaction is less than 1 kcal/mole. However, since
the water molecule itself has a substantial dipole moment and is present in
large amounts, ion-dipole interactions can be important factors in protein
structures.
Whereas the static aspects of electrostatic interactions can be readily for-
mulated, the dynamics are more difficult to ascertain. A few kinetic studies
of ion-pair formation have been carried out, and the rate constants appear
to be those of diffusion-controlled reactions. The diffusion-controlled rate
constants for association and dissociation reactions, k and k , respectively,
f d
1 Protein Strucutre and Dynamics 3
can be approximated as (7)
k= 4π£> ,a i — (1-1)
f ΑΒ
J 1000
K = 3£>AB/ eW(a)lkT] (1-2)
a2
(«r -1
/ = VjkT "r \
r2J
4na3N
K = kf/kd -" ~~ wi0n -e~ U(a)/kT (1-3)
In these equations, D is the sum of the diffusion constants of the two
AB
reactants, a is the distance of closest approach of the reactants, U is the
potential energy of interaction between the two reactants, k is Boltzmann's
constant, and N is Avogadro's number. For reactions between small
0
molecules with univalent charges of opposite sign, k — 1010 M"1 sec"1
f
and k ~ 1010 sec-1. As is amplified later for hydrogen-bonding reactions,
d
this implies that the unimolecular rate constants for ion-ion interactions are
greater than 1010 sec"i. A model for ion-dipole interactions is the solvation
of metal ions by water. For water interactions with alkali metals, the char-
acteristic rate constants for first hydration shell solvation are about 109 sec"x.
However, for higher valence metals, the water-metal dissociation rate can be
considerably slower, and in extreme cases (e.g., Cr3 + ) can be many hours.
These slower rates are not likely to be relevant in proteins.
Another type of electrostatic interaction of great importance in proteins
is the hydrogen bond. Some typical hydrogen bonds and lengths are illus-
trated in Table 1-2. In nonhydrogen-bonding solvents, typical enthalpies of
formation are a few kilocalories per hydrogen bond per mole. For example,
Table 1-2
Some Typical Hydrogen Bonds and
Bond Lengths
Hydrogen bond Bond length (Â)
OH O 2.7
OH ■N 2.9
NH O 3.0
NH· •N 3.1
4 1 Protein Structure and Dynamics
in CHCI3 the dimerization of 2-pyridone
2
Π *
(1-4)
O H N \/
has an equilibrium constant of 150 M'1 and an enthalpy change of —5.9
kcal/mole (2). However, in water hydrogen bond formation between solutes
is not as favorable because water competes for the hydrogen bonds. Both
the standard free energy changes and enthalpy changes for hydrogen bond
formation are close to zero in water. In a protein, hydrogen bonds may be
shielded from water and, therefore, may be quite stable. This stability is due
to the creation of a special structure of the protein. Energetically this means
that the stability of the hydrogen bond has been paid for by the energy
required for a specific protein conformation. Hydrogen bonding can provide
great specificity because of the different possible types of hydrogen bonds
and the strong preference for linear bonding.
The dynamics of hydrogen bonding have been studied in a variety of
model systems. Some typical data for the dimerization of 2-pyridone in
weakly hydrogen-bonding solvents are presented in Table 1-3. In relatively
weakly hydrogen-bonding solvents, such as the first four entries in Table 1-3,
the association rate is essentially diffusion-controlled, whereas the associa-
tion rate constants for the last two entries are considerably less than expected
for a diffusion-controlled process. This can be understood in terms of the
mechanism
2P ^=^ p . p ^=± p—p ^=^ ρ=ρ (1-5)
fc-1 k-2 k-3
where P represents pyridone, P · · P is a nonhydrogen-bonded dimer that
Table 1-3
Thermodynamic and Kinetic Parameters for the Dimerization of 2-Pyridone
AG° AH° 10-% 10~7 kr
Solvent (k<: al/mole) (kc: al/mole) (M_1 sec-1 ) (sec-1) Reference
CHCI3 -3.0 -5.9 3.3 2.2 2
50 wt % dioxane-CCl -2.5 -4.6 2.1 2.9 3
4
Dioxane -1.6 -1.7 2.1 13.0 4
1% Water-dioxane -1.3 — 1.7 17.0 4
CCl -dimethyl sulfoxide
4
(1.1 m) -0.4 — 0.26 14.8 3
CCl -dimethyl sulfoxide
4
(5.5 m) 0.9 — 0.069 2.7 3
1 Protein Structure and Dynamics 5
forms and dissociates by diffusion-controlled rates, P—P is the dimer with
one hydrogen bond formed, and P=P is the complex with two hydrogen
bonds formed. If the intermediates are assumed to be in a steady state, the
observed rate constants for association and dissociation, k and /c, are
f r
kf = i + (k^/k )(i + k_ /k ) (1"6)
2 2 3
fc'=l+(* /*-2)(l+*2/*-l) (K7)
3
If the reaction is diffusion-controlled, k « k ; this is the case when k > /c_
f 1 2 l5
i.e., when desolvation of the solute and formation of the first hydrogen bond
is faster than diffusion apart of the reactions. Since the value of/c_ is about
x
1010 sec-1, the actual rate constant for hydrogen bond formation, k , must
2
have a value of 1011—1012 sec-1. For the last two entries in Table 1-3, the
solvent can form strong hydrogen bonds so the association rate is no longer
diffusion-controlled. In these cases, desolvation of the solute is rate deter-
mining with a specific rate constant of about 108 sec"1. In fact, this rate
constant is characteristic of most solvation-desolvation processes involving
hydrogen bonds. Thus, the rate constant for the making and breaking of
single hydrogen bonds in water is >108 sec"1. Note that when the dimer
formation is diffusion-controlled, k = /c_ (/c_ /^ )(/c_ //c ). Since k^ is
r 1 2 2 3 3 x
about the same in all cases, k is a measure of the thermodynamic stability
r
of the two pyridone-pyridone hydrogen bonds relative to pyridone-solvent
interactions.
Hydrophobie interactions are usually rather loosely defined to describe
what happens when hydrocarbons are put into water. Actually several types
of interactions should be distinguished. Hydrocarbons interact very weakly
with each other due to dispersion forces. Also, planar pi electron systems
tend to stack on top of each other. Both of these interactions are very short
range. When hydrocarbons are put into water, the dominant factor is that
hydrocarbons and water do not like to associate. Thus, if a hydrocarbon is
solubilized by water, the water tends to form a sheaf around the hydrocarbon
in which the water dipoles are strongly oriented through hydrogen bonding.
The free energy associated with such interactions can be estimated from
measurements of the free energy for the transfer of hydrocarbons from water
to a nonpolar solvent. For example, the free energies of transfer for a méthy-
lène group and aromatic ring are about — 0.7 kcal/mole and — 2 kcal/mole,
respectively (5). If two hydrophobic molecules are present in water, they
tend to associate, not because of the strong interactions between the hydro-
phobic molecules, but because some of the oriented water molecules are
